# 35. Construct a Triangle Given the Angle Opposite Its Base and the Sum and Product of the Two Other Sides

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This Demonstration shows how to construct a triangle given the angle opposite the side , the sum of the lengths of the other two sides and their product . The numbers and satisfy the quadratic equation . The problem is solved graphically using Carlyle's circle.

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Contributed by: Izidor Hafner and Marko Razpet (September 2018)

Open content licensed under CC BY-NC-SA

## Details

This task is posed as problem 471 in [1].

Reference

[1] L. H. von Holleben and P. Gerwien, *Aufgaben-Systeme und Sammlungen aus der Ebenen Geometrie: Aufgaben*, Vols. I and II, Berlin: G. Reimer, 1831 and 1832.

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